Factorization, coherence, and asymmetry in the Heisenberg spin- 12 XXZ chain with Dzyaloshinskii-Moriya interaction in transverse magnetic field

Abstract

We investigate the factorization, coherence, and asymmetry properties of the one-dimensional Heisenberg spin-$\frac{1}{2}$ XXZ chain with Dzyaloshinskii-Moriya interaction (DMI) and a transverse magnetic field using quantum information measures. Both longitudinal and transverse DM vectors are considered. Using numerical DMRG methods, we compute bipartite entanglement estimators like the one-tangle, two-spin concurrence and quantum coherence estimators like the Wigner-Yanase-skew information. We show that a longitudinal DMI destroys the factorizability property while a transverse DMI preserves it. We relate the absence of factorizability to the breaking of the $U(1)$ rotation symmetry about the local magnetization axis at each lattice site. Physically, the breaking of the symmetry manifests in the existence of a chiral current. Furthermore, we show that although the longitudinal DMI destroys the factorization property, there is a ``pseudofactorizing'' field at which the entanglement and hence violation of the $U(1)$ symmetry is minimal. Our calculations indicate a phase coherent ground state at ${h}_{\text{pf}}$. An entanglement transition (ET) occurs across this field which is characterized by an enhanced but finite range of two-spin concurrence in its vicinity in contrast with the diverging range of the concurrence for the ET across the factorizing field. We relate the asymmetry to the ``frameness'' or the ability for the state to act as a reference frame for some measurement. In the absence of the longitudinal DMI (or in the presence of a transverse DMI), at the factorizing field, the single site magnetization axis serves to specify the common $z$ axis for the full system but not the full Cartesian reference frame due to a lack of phase reference. On the other hand, in the presence of a longitudinal DMI, our results indicate that at the pseudofactorizing field, the local magnetization and the chiral current are sufficient to specify the full Cartesian reference frame with the chiral current serving as the macroscopic quantity to determine the phase reference.